Page 377 - Schaum's Outline of Differential Equations

360 ANSWERS TO SUPPLEMENTARY PROBLEMS

19.15. Method: MODIFIED EULER'S METHOD

Problem:

ft = 0.2
x n
True solution
Y(x) = x^9 + \nx 2
#y n y n
1.0 — 3.0000 3.0000

1.2 3.6667 3.6716 3.6722
1.4 4.3489 4.3530 4.3542
1.6 5.0393 5.0429 5.0444

1.8 5.7367 5.7399 5.7419

2.0 6.4404 6.4432 6.4456

2
19.16. The true solution is Y(x) = x /2- 1, a second-degree polynomial. Since the modified Euler's method is a second-
order method, it will generate the exact solution.

19.17. Method: MODIFIED EULER'S METHOD

3
Problem: / = -4.x ;y(2) = 6
ft = 0.2
x n
True solution
4
py n y n Y(x) = x - 10
2.0 — 6.0000 6.0000
2.2 12.4000 13.4592 13.4256

2.4 21.9776 23.2480 23.1776
2.6 34.3072 35.8080 35.6976
2.8 49.8688 51.6192 51.4656

3.0 69.1808 71.2000 71.0000